Simulating the Earth’s radiation belts: internal acceleration and continuous losses to the magnetopause

In the Earth's radiation belts the flux of relativistic electrons is highly variable, sometimes changing by orders of magnitude within a few hours. Since energetic electrons can damage satellites it is important to understand the processes driving these changes and, ultimately, to develop forecasts of the energetic electron population. One approach is to use 3-dimensional diffusion models, based on a Fokker-Planck equation. Here we describe a model where the phase-space density is set to zero at the outer L* boundary, simulating losses to the magnetopause, using recently published chorus diffusion coefficients for 1.5 ≤ L* ≤ 10. The value of the phase-space density on the minimum energy boundary is determined from a recently published, solar wind dependent, statistical model. Our simulations show that an outer radiation belt can be created by local acceleration of electrons from a very soft energy spectrum without the need for a source of electrons from inward radial transport. The location in L* of the peaks in flux for these steady state simulations is energy dependent and moves Earthward with increasing energy. Comparisons between the model and data from the CRRES satellite are shown; flux drop-outs are reproduced in the model by the increased outward radial diffusion that occurs during storms. Including the inward movement of the magnetopause in the model has little additional effect on the results. Finally, the location of the low energy boundary is shown to be important for accurate modelling of observations

Extreme relativistic electron fluxes at geosynchronous orbit: Analysis of GOES E > 2 MeV electrons

Relativistic electrons (E > 1 MeV) cause internal charging on satellites and are an important space weather hazard. A key requirement in space weather research concerns extreme events and knowledge of the largest flux expected to be encountered over the lifetime of a satellite mission. This is interesting both from a scientific and practical point of view since satellite operators, engineers and the insurance industry need this information to better evaluate the effects of extreme events on their spacecraft. Here we conduct an extreme value analysis of daily averaged E > 2 MeV electron fluxes from the Geostationary Operational Environmental Satellites (GOES) during the 19.5 year period from 1 January 1995 to 30 June 2014. We find that the daily averaged flux measured at GOES West is typically a factor of ~2.5 higher than that measured at GOES East and we conduct independent analyses for these two locations. The 1 in 10, 1 in 50 and 1 in 100 year daily averaged E > 2 MeVelectron fluxes at GOES West are 1.84×105, 5.00×105 and 7.68×105 cm−2s−1sr−1 respectively. The corresponding fluxes at GOES East are 6.53×104, 1.98×105 and 3.25×105 cm−2s−1sr−1 respectively. The largest fluxes seen during the 19.5 year period on 29 July 2004 were particularly extreme and were seen by satellites at GOES West and GOES East. The extreme value analysis suggests that this event was a 1 in 50 year event

Physiotherapy rehabilitation for osteoporotic vertebral fracture (PROVE) : study protocol for a randomised controlled trial

Background: Osteoporosis and vertebral fracture can have a considerable impact on an individual’s quality of life. There is increasing evidence that physiotherapy including manual techniques and exercise interventions may have an important treatment role. This pragmatic randomised controlled trial will investigate the clinical and cost-effectiveness of two different physiotherapy approaches for people with osteoporosis and vertebral fracture, in comparison to usual care. Methods/Design: Six hundred people with osteoporosis and a clinically diagnosed vertebral fracture will be recruited and randomly allocated to one of three management strategies, usual care (control - A), an exercise-based physiotherapy intervention (B) or a manual therapy-based physiotherapy intervention (C). Those in the usual care arm will receive a single session of education and advice, those in the active treatment arms (B + C) will be offered seven individual physiotherapy sessions over 12 weeks. The trial is designed as a prospective, adaptive single-blinded randomised controlled trial. An interim analysis will be completed and if one intervention is clearly superior the trial will be adapted at this point to continue with just one intervention and the control. The primary outcomes are quality of life measured by the disease specific QUALLEFO 41 and the Timed Loaded Standing test measured at 1 year. Discussion: There are a variety of different physiotherapy packages used to treat patients with osteoporotic vertebral fracture. At present, the indication for each different therapy is not well defined, and the effectiveness of different modalities is unknown

An investigation of VLF transmitter wave power in the inner radiation belt and slot region

Signals from man‐made Very Low Frequency (VLF) transmitters, used for communications with submarines, can leak into space and contribute to the dynamics of energetic electrons in the inner radiation belt and slot region. In this study we use ∼5 years of plasma wave data from the Van Allen Probe A satellite to construct new models of the observed wave power from VLF transmitters both as a function of L* and magnetic local time and geographic location. Average power peaks primarily on the nightside of the Earth for the VLF transmitters at low geographic latitudes. At higher latitudes the peak average power extends further in magnetic local time due to more extensive periods of nighttime in the winter months. Nighttime power is typically orders of magnitude more than that observed near noon, implying that loss rates from a given VLF transmitter will also maximize in this region. The observed power from any given VLF transmitter is tightly confined in longitude, with the nightside peak power typically falling by a factor of 10 within 10° longitude of the location of the peak signal. We show that the total average wave power from all VLF transmitters lies in the range 3–9 pT2 in the region 1.3<L*<3.0, with approximately 50% of this power emanating from three VLF transmitters, NWC, NAA, and DHO38

Quasi-linear simulations of inner radiation belt electron pitch angle and energy distributions

“Peculiar” or “butterfly” electron pitch angle distributions (PADs), with minima near 90°, have recently been observed in the inner radiation belt. These electrons are traditionally treated by pure pitch angle diffusion, driven by plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter signals. Since this leads to monotonic PADs, energy diffusion by magnetosonic waves has been proposed to account for the observations. We show that the observed PADs arise readily from two-dimensional diffusion at L = 2, with or without magnetosonic waves. It is necessary to include cross diffusion, which accounts for the relationship between pitch angle and energy changes. The distribution of flux with energy is also in good agreement with observations between 200 keV and 1 MeV, dropping to very low levels at higher energy. Thus, at this location radial diffusion may be negligible at subrelativistic as well as ultrarelativistic energy

Effects of VLF transmitter waves on the inner belt and slot region

Signals from very low frequency (VLF) transmitters can leak from the Earth‐ionosphere wave guide into the inner magnetosphere, where they propagate in the whistler mode and contribute to electron dynamics in the inner radiation belt and slot region. Observations show that the waves from each VLF transmitter are highly localized, peaking on the nightside in the vicinity of the transmitter. In this study we use ∼5 years of Van Allen Probes observations to construct global statistical models of the bounce‐averaged pitch angle diffusion coefficients for each individual VLF transmitter, as a function of L*, magnetic local time (MLT), and geographic longitude. We construct a 1‐D pitch angle diffusion model with implicit longitude and MLT dependence to show that VLF transmitter waves weakly scatter electrons into the drift loss cone. We find that global averages of the wave power, determined by averaging the wave power over MLT and longitude, capture the long‐term dynamics of the loss process, despite the highly localized nature of the waves in space. We use our new model to assess the role of VLF transmitter waves, hiss waves, and Coulomb collisions on electron loss in the inner radiation belt and slot region. At moderate relativistic energies, E∼500 keV, waves from VLF transmitters reduce electron lifetimes by an order of magnitude or more, down to the order of 200 days near the outer edge of the inner radiation belt. However, VLF transmitter waves are ineffective at removing multi–megaelectron volt electrons from either the inner radiation belt or slot region

Particle-in-cell experiments examine electron diffusion by whistler-mode waves: 1. Benchmarking with a cold plasma

Using a particle-in-cell code, we study the diffusive response of electrons due to wave particle interactions with whistler-mode waves. The relatively simple configuration of field-aligned waves in a cold plasma is used in order to benchmark our novel method, and to compare with previous works that used a different modelling technique. In this boundary-value problem, incoherent whistler-mode waves are excited at the domain boundary, and then propagate through the ambient plasma. Electron diffusion characteristics are directly extracted from particle data across all available energy and pitch-angle space. The ‘nature’ of the diffusive response is itself a function of energy and pitch-angle, such that the rate of diffusion is not always constant in time. However, after an initial transient phase, the rate of diffusion tends to a constant, in a manner that is consistent with the assumptions of quasilinear diffusion theory. This work establishes a framework for future investigations on the nature of diffusion due to whistler-mode wave-particle interactions, using particle-in-cell numerical codes with driven waves as boundary value problems

Electron losses from the radiation belts caused by EMIC waves

Electromagnetic Ion Cyclotron (EMIC) waves cause electron loss in the radiation belts by resonating with high energy electrons at energies greater than about 500 keV. However, their effectiveness has not been fully quantified. Here we determine the effectiveness of EMIC waves by using wave data from the fluxgate magnetometer on CRRES to calculate bounce averaged pitch angle and energy diffusion rates for L* =3.5 - 7 for five levels of Kp between 12 - 18 MLT. To determine the electron loss EMIC diffusion rates were included in the BAS Radiation Belt Model together with whistler mode chorus, plasmaspheric hiss and radial diffusion. By simulating a 100 day period in 1990 we show that EMIC waves caused a significant reduction in the electron flux for energies greater than 2 MeV but only for pitch angles lower than about 60°.The simulations show that the distribution of electrons left behind in space looks like a pancake distribution. Since EMIC waves cannot remove electrons at all pitch angles even at 30 MeV, our results suggest that EMIC waves are unlikely to set an upper limit on the energy of the flux of radiation belt electrons

Extreme internal charging currents in medium Earth orbit: Analysis of SURF plate currents on Giove-A

Relativistic electrons can penetrate spacecraft shielding and can damage satellite components. Spacecraft in medium Earth orbit pass through the heart of the outer radiation belt and may be exposed to large fluxes of relativistic electrons, particularly during extreme space weather events. In this study we perform an extreme value analysis of the daily average internal charging currents at three different shielding depths in medium Earth orbit as a function of L∗ and along the orbit path. We use data from the SURF instrument on board the European Space Agency's Giove-A spacecraft from December 2005 to January 2016. The top, middle, and bottom plates of this instrument respond to electrons with energies >500 keV, >700 keV, and >1.1 MeV, respectively. The 1 in 10 year daily average top plate current decreases with increasing L∗ ranging from 1.0 pA cm−2 at L∗=4.75 to 0.03 pA cm−2 at L∗=7.0. The 1 in 100 year daily average top plate current is a factor of 1.2 to 1.8 larger than the corresponding 1 in 10 year current. The 1 in 10 year daily average middle and bottom plate currents also decrease with increasing L∗ ranging from 0.4 pA cm−2 at L∗=4.75 to 0.01 pA cm−2 at L∗=7.0. The 1 in 100 year daily average middle and bottom plate currents are a factor of 1.2 to 2.7 larger than the corresponding 1 in 10 year currents. Averaged along the orbit path the 1 in 10 year daily average top, middle, and bottom plate currents are 0.22, 0.094, and 0.094 pA cm−2, respectively